Rivers were a set of extra routes through some provinces, as you
guessed. They didn't impede land movement, although, as the Oly I
map was hand-created and somewhat ... irregular, there were actually
some paths where there was a river route but no corresponding land
route.

Instead of getting on a ship, though, for river travel you just needed
so many small boats to be able to go over the river link. River travel
and ocean ship travel were incompatible.

The Oly II map is sketched out by me at a high level (I draw the
continents), but filled in by a program.